There is general familiarity with a compass or a simple horseshoe magnet. However, does any one wonder why in the simple refrigerator magnet, the magnetism exists only on one side and not on the other? It is a simple arrangement in the construction of the magnet that allows magnetic field to only to be present on one side of the magnet. This arrangement is known as the Halbach effect. The theory behind this effect was originally discussed by J. C. Mallinson in 1973, who mathematically proved that it is possible to construct a magnet such that that a magnetic flux would exist just on one side of the magnet.
Picture a single, long bar magnet with your standard North and South poles at each end. Now slice this magnet up into several even, smaller pieces and you will end up with several smaller magnets, each with its own North and South Pole. Arrange these pieces side-by-side so that each consecutive piece's North Pole has been rotated a quarter turn from the previous magnet. What you will end up with is the same bar magnet; however, the direction of magnetization will be rotating uniformly as you progress in a particular direction. The name for this magnet is a Halbach array, after the physicist Klaus Halbach who invented it.
Generally a Halbach array is an arrangement of permanent magnets that can augment the magnetic field on one side of the Halbach array while canceling the magnetic field to near zero or substantially near zero on the other side of the Halbach array. As illustrated in FIGS. 1A and 1B, the magnetic field can be enhanced on the bottom side of the Halbach array and cancelled on the top side (a one-sided flux) of the Halbach array. The quarter turn rotating pattern of permanent magnets (on the front face; on the left, up, right, down) can be continued indefinitely and have the same effect. This arrangement can result in roughly similar to many horseshoe magnets placed adjacent to each other, and with similar poles touching.
The magnetic flux diagram shown in FIGS. 1A and 1B clearly demonstrates the one sided flux. Some advantages of one sided flux distributions can be at least the following:
The field can be twice as large on the side on which the flux is confined (in the idealized case).
Stray fields are not likely produced (in the ideal, infinite length case) on the opposite side. This can be helpful with field confinement, which can usually be a problem in the design of magnetic structures.
However in a realistic scenario, the field of a Halbach array may be anywhere between 1.2-1.4 times of a bar magnet of similar dimensions. Several designs of electric motors using the Halbach array have been reported in the literature.